scholarly journals Effective Pedagogy of Guiding Undergraduate Engineering Students Solving First-Order Ordinary Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1623
Author(s):  
William Guo ◽  
Wei Li ◽  
Christopher C. Tisdell
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Teaching And Learning ◽  
Engineering Students ◽  
Advanced Mathematics ◽  
Order Linear ◽  
First Order ◽  
Undergraduate Engineering ◽  
Pedagogical Design ◽  
Linear Odes

An alternative pedagogical design is discussed that aims to guide engineering students to solve first-order ordinary differential equations (ODEs), and is based on students’ learning weaknesses identified from previous teaching and learning activities. This approach supported student’s self-enrichment through exploration of relevant resources in ODEs, and guided students towards the choice of their own effective ways for solving ODEs for different problems. This paper presents the practices on designing and delivering solution techniques for first-order linear ODEs using this approach for more than 400 undergraduate engineering students at a regional university in Australia during 2014–2017. The timeline involved initial experimentation in 2014 and 2015, followed by refinements to the pedagogy based on student’s feedback. The refined pedagogy was then used for the advanced mathematics course in 2016 and 2017. Significant improvements were made in student’s learning outcomes in effectively and accurately solving the first-order linear ODEs over this period.

Remark on Algorithm 982: Explicit Solutions of Triangular Systems of First-order Linear Initial-value Ordinary Differential Equations with Constant Coefficients

2022 ◽  
Vol 48 (1) ◽  
pp. 1-4
Author(s):  
W. Van Snyder
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Coefficient Matrix ◽  
Explicit Solutions ◽  
Initial Value ◽  
Singular Coefficient ◽  
Order Linear ◽  
First Order ◽  
Triangular Systems ◽  
Constant Coefficients

Algorithm 982: Explicit solutions of triangular systems of first-order linear initial-value ordinary differential equations with constant coefficients provides an explicit solution for an homogeneous system, and a brief description of how to compute a solution for the inhomogeneous case. The method described is not directly useful if the coefficient matrix is singular. This remark explains more completely how to compute the solution for the inhomogeneous case and for the singular coefficient matrix case.

scholarly journals Uma proposta de ensino de equação diferencial no curso de Engenharia Civil à luz da teoria matemática no contexto das ciências

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
ALESSANDRO ROSA SILVA ◽  
GABRIEL LOUREIRO DE LIMA
Keyword(s):  
Higher Education ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Teaching And Learning ◽  
Civil Engineering ◽  
Teaching Sequence ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Doctoral Work

ResumoApresentamos por meio deste artigo o trabalho de doutorado que estamos desenvolvendo com o objetivo de discutir o ensino e a aprendizagem de Equações Diferenciais Ordinárias lineares de 1ª e 2ª ordens em um curso de Engenharia Civil, sob à luz da Matemática no Contexto das Ciências. A pesquisa encontra-se atualmente na fase da análise de livros textos utilizados como referências principais nas disciplinas não matemáticas do curso citado, guiada pela etapa central da metodologia Dipcing, inserida em uma das fases da MCC, a curricular. Identificaremos, a partir desta análise, situações-problemas do contexto da Engenharia Civil que mobilizam EDO lineares de 1ª e 2ª ordens. Tais situações nos servirão de base para a construção de uma sequência de ensino contextualizando as EDO na Engenharia Civil. Os problemas propostos serão trabalhados em sala de aula e posteriormente analisaremos os resultados, em termos de aprendizagem, obtidos por meio da sequência de ensino desenvolvida. Palavras-Chave: Ensino Superior; Engenharia; Equações Diferenciais Ordinárias; Matemática no Contexto das Ciências.AbstractWe present, by means of this article, the doctoral work we are developing with the objective of discussing the teaching and learning of 1st and 2nd order linear Ordinary Differential Equations in a Civil Engineering course under the light of Mathematics in the Context of Sciences. The research is currently in the phase of the analysis of textbooks used as main references in the non-mathematical disciplines of the mentioned course, guided by the central stage of the methodology Dipcing, inserted in one of the phases of the MCC, the curricular. We will identify, from this analysis, situations-problems of the Civil Engineering context that mobilize linear ORDs of 1st and 2nd orders. Such situations will serve as a basis for the construction of a teaching sequence contextualizing the ODE in Civil Engineering. The problems proposed will be worked in the classroom and later we will analyze the results, in terms of learning, obtained through the developed teaching sequence.Keywords: Higher Education; Engineering; Ordinary Differential Equations; Mathematics in the Context of Science. 

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